Abstract
We determine the orders of the canonical elements in K O KO -rings of quaternionic spherical space forms S 4 n + 3 / Q k {S^{4n + 3}}/{Q_k} and apply them to prove the nonexistence theorems of immersions and embeddings of S 4 n + 3 / Q k {S^{4n + 3}}/{Q_k} in Euclidean spaces.
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